Marcus Paige added 16 points and Justin Jackson had 13. The Tar Heels (8-2) won their first game without injured big man Kennedy Meeks and bounced back from a last-second loss at Texas that knocked them out of the top 10.
Joel Berry II had 12 points and Isaiah Hicks finished with 11 for North Carolina, which never trailed, shot 50 percent and built a 43-33 rebounding advantage.
Louis Dabney scored 18 points for Tulane (6-5), which pulled to 70-55 on Malik Morgan's jumper with just over 8 minutes left.
The Tar Heels countered with 15 straight points -- a burst that started with Johnson's jumper, included two 3-pointers from Paige and made it a 30-point game.
Rebounding was a point of emphasis in this one for the Tar Heels, who managed just four offensive boards -- their fewest in 13 seasons under coach Roy Williams -- in the loss to the Longhorns.
North Carolina also didn't have Meeks, who trails only Johnson among Tar Heels in rebounding but is out at least two weeks with a bone bruise in his left knee. Meeks averaged 12.3 points and 7.4 rebounds while starting the first nine games.
North Carolina gave 6-foot-11 senior Joel James his first start of the season, then turned Johnson loose on the Green Wave. He had 17 points in the first half -- one more than his previous best this season -- and surpassed his prior career best of 24 set in 2013 against Richmond.
Theo Pinson finished with 10 points for the Tar Heels.
Tulane: The Green Wave fell to 11-50 against Top 25 opponents since 1989 and haven't beaten the Tar Heels since 1927 -- by a 20-19 score -- while losing 12 straight in the series.
North Carolina: Tulane assistant Shammond Williams returned to Chapel Hill for the first time as a coach. Williams played for the Tar Heels from 1994-98 and set the school's career record with 233 3-pointers -- a mark that was broken in the Texas game by Paige. Both were honored before the game.
North Carolina plays UCLA on Saturday in Brooklyn, New York.